If time had no beginning

Abstract: General Relativity traces the evolution of our Universe back to a Big Bang singularity. To probe physics before the singularity -- if indeed there is a ``before'' -- we must turn to quantum gravity. The Causal Set approach to quantum gravity provides us with a causal structure in the absence of the continuum, thus allowing us to go beyond the Big Bang and consider cosmologies in which time has no beginning. But is a time with no beginning in contradiction with a passage of time? In the Causal Set approach, the passage of time is captured by a process of spacetime growth. We describe how to adapt this process for causal sets in which time has no beginning and discuss the consequences for the nature of time.

• The paper introduces a revised Causal Set Theory model that allows a past-infinite causal set by enabling new elements to precede existing ones.
• It adapts covariant growth processes using convex stems to represent past-infinite spacetime, challenging the limitations of General Relativity.
• The authors propose a novel concept of asynchronous becoming, bridging traditional time passage with an infinite temporal framework in quantum gravity.

Insights on "If Time Had No Beginning"

The paper "If time had no beginning," authored by Bruno Valeixo Bento and Stav Zalel, presents a detailed exploration of the concept of time within the framework of Causal Set Theory (CST), an active area of research in quantum gravity. The paper tackles a fundamental question: What happens to our understanding of time if the conventional notion of a temporal beginning is eschewed?

Abstract and Theoretical Background

The authors begin by highlighting the inadequacy of General Relativity (GR) in describing the universe at the Big Bang singularity—a point where known physical laws break down. Exploring pre-Big Bang physics requires exploring quantum gravity, for which Causal Set Theory provides a promising framework. CST posits a discrete spacetime structure composed of fundamental, indivisible units arranged in a partially ordered set that furnishes a causal structure independent of the continuum.

Main Contributions

The paper posits the possibility of cosmologies with no temporal beginning by adapting CST's spacetime growth models. The authors address two pivotal questions: Can time be infinite without conflicting with its passage as captured by CST's growth dynamics, and what are the implications of such a perspective?

1. Sequential vs. Covariant Growth Dynamics: Traditional models like the Classical Sequential Growth (CSG) are constrained by time having a beginning, due to the restriction that new elements cannot precede existing ones. The paper suggests modifying these dynamics to accommodate a time without a beginning. The revised framework allows newly born elements to precede existing elements, effectively enabling a past-infinite structure.
2. Covariant Growth for Past-Infinite Causal Sets: The paper introduces an adjustment to covariant growth processes that accommodate causal sets with no temporal beginning. This involves considering convex rather than merely finite portions (stems) of the causal set, enabling a plausible description of past-infinite causal sets within CST.
3. Relating Asynchronous Becoming to Growth: The authors speculate on a "vagueness" associated with covariant growth, proposing it as a potential bridge to reconciling our intuitive understanding of becoming with a past-infinite temporality. This perspective challenges the intuitive notion of time’s passage while suggesting a novel paradigm that might address asynchronous becoming.

Implications and Future Directions

This work advances the theoretical underpinnings of CST by expanding its applicability to models where time has no inception. It challenges existing paradigms of time in physics, potentially reshaping cosmological models by allowing for a truly infinite past. The implications for understanding cosmological phenomena and the evolution of the universe are profound, though the complexities of ascribing physical dynamics to such constructs remain.

For future research, the authors propose that a deeper mathematical and conceptual understanding of asynchronous becoming is necessary. Further, establishing how this growth model aligns with existing quantum gravitational theories and observational data would provide insights into fundamental questions about the nature of time and spacetime itself.

In conclusion, this paper opens intriguing avenues in the conceptualization of time, pushing the boundaries of both theoretical physics and cosmology. By postulating time's absence of inception, Bento and Zalel encourage a profound reevaluation of conventional physics, which may lead to significant developments in quantum gravity research.